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Order Exponent Nilpotency class Nilpotent
Center Commutator Central quotient Abelianization
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Automorphism group Automorphisms Transitive degree Permutation degree
Minimal degree of $\C$-irrep Minimal degree of $\Q$-irrep Minimal degree of $\C$-rep Minimal degree of $\Q$-rep
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Results (1-50 of 1315 matches)

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Label Name Order Exponent $\card{\mathrm{conj}(G)}$ Center Central quotient Commutator Abelianization Type - length
6.2 $C_6$ $2 \cdot 3$ $2 \cdot 3$ $6$ $C_6$ $C_1$ $C_1$ $C_{6}$ Cyclic
10.2 $C_{10}$ $2 \cdot 5$ $2 \cdot 5$ $10$ $C_{10}$ $C_1$ $C_1$ $C_{10}$ Cyclic
14.2 $C_{14}$ $2 \cdot 7$ $2 \cdot 7$ $14$ $C_{14}$ $C_1$ $C_1$ $C_{14}$ Cyclic
15.1 $C_{15}$ $3 \cdot 5$ $3 \cdot 5$ $15$ $C_{15}$ $C_1$ $C_1$ $C_{15}$ Cyclic
21.2 $C_{21}$ $3 \cdot 7$ $3 \cdot 7$ $21$ $C_{21}$ $C_1$ $C_1$ $C_{21}$ Cyclic
22.2 $C_{22}$ $2 \cdot 11$ $2 \cdot 11$ $22$ $C_{22}$ $C_1$ $C_1$ $C_{22}$ Cyclic
26.2 $C_{26}$ $2 \cdot 13$ $2 \cdot 13$ $26$ $C_{26}$ $C_1$ $C_1$ $C_{26}$ Cyclic
30.4 $C_{30}$ $2 \cdot 3 \cdot 5$ $2 \cdot 3 \cdot 5$ $30$ $C_{30}$ $C_1$ $C_1$ $C_{30}$ Cyclic
33.1 $C_{33}$ $3 \cdot 11$ $3 \cdot 11$ $33$ $C_{33}$ $C_1$ $C_1$ $C_{33}$ Cyclic
34.2 $C_{34}$ $2 \cdot 17$ $2 \cdot 17$ $34$ $C_{34}$ $C_1$ $C_1$ $C_{34}$ Cyclic
35.1 $C_{35}$ $5 \cdot 7$ $5 \cdot 7$ $35$ $C_{35}$ $C_1$ $C_1$ $C_{35}$ Cyclic
38.2 $C_{38}$ $2 \cdot 19$ $2 \cdot 19$ $38$ $C_{38}$ $C_1$ $C_1$ $C_{38}$ Cyclic
39.2 $C_{39}$ $3 \cdot 13$ $3 \cdot 13$ $39$ $C_{39}$ $C_1$ $C_1$ $C_{39}$ Cyclic
42.6 $C_{42}$ $2 \cdot 3 \cdot 7$ $2 \cdot 3 \cdot 7$ $42$ $C_{42}$ $C_1$ $C_1$ $C_{42}$ Cyclic
46.2 $C_{46}$ $2 \cdot 23$ $2 \cdot 23$ $46$ $C_{46}$ $C_1$ $C_1$ $C_{46}$ Cyclic
51.1 $C_{51}$ $3 \cdot 17$ $3 \cdot 17$ $51$ $C_{51}$ $C_1$ $C_1$ $C_{51}$ Cyclic
55.2 $C_{55}$ $5 \cdot 11$ $5 \cdot 11$ $55$ $C_{55}$ $C_1$ $C_1$ $C_{55}$ Cyclic
57.2 $C_{57}$ $3 \cdot 19$ $3 \cdot 19$ $57$ $C_{57}$ $C_1$ $C_1$ $C_{57}$ Cyclic
58.2 $C_{58}$ $2 \cdot 29$ $2 \cdot 29$ $58$ $C_{58}$ $C_1$ $C_1$ $C_{58}$ Cyclic
62.2 $C_{62}$ $2 \cdot 31$ $2 \cdot 31$ $62$ $C_{62}$ $C_1$ $C_1$ $C_{62}$ Cyclic
65.1 $C_{65}$ $5 \cdot 13$ $5 \cdot 13$ $65$ $C_{65}$ $C_1$ $C_1$ $C_{65}$ Cyclic
66.4 $C_{66}$ $2 \cdot 3 \cdot 11$ $2 \cdot 3 \cdot 11$ $66$ $C_{66}$ $C_1$ $C_1$ $C_{66}$ Cyclic
69.1 $C_{69}$ $3 \cdot 23$ $3 \cdot 23$ $69$ $C_{69}$ $C_1$ $C_1$ $C_{69}$ Cyclic
70.4 $C_{70}$ $2 \cdot 5 \cdot 7$ $2 \cdot 5 \cdot 7$ $70$ $C_{70}$ $C_1$ $C_1$ $C_{70}$ Cyclic
74.2 $C_{74}$ $2 \cdot 37$ $2 \cdot 37$ $74$ $C_{74}$ $C_1$ $C_1$ $C_{74}$ Cyclic
77.1 $C_{77}$ $7 \cdot 11$ $7 \cdot 11$ $77$ $C_{77}$ $C_1$ $C_1$ $C_{77}$ Cyclic
78.6 $C_{78}$ $2 \cdot 3 \cdot 13$ $2 \cdot 3 \cdot 13$ $78$ $C_{78}$ $C_1$ $C_1$ $C_{78}$ Cyclic
82.2 $C_{82}$ $2 \cdot 41$ $2 \cdot 41$ $82$ $C_{82}$ $C_1$ $C_1$ $C_{82}$ Cyclic
85.1 $C_{85}$ $5 \cdot 17$ $5 \cdot 17$ $85$ $C_{85}$ $C_1$ $C_1$ $C_{85}$ Cyclic
86.2 $C_{86}$ $2 \cdot 43$ $2 \cdot 43$ $86$ $C_{86}$ $C_1$ $C_1$ $C_{86}$ Cyclic
87.1 $C_{87}$ $3 \cdot 29$ $3 \cdot 29$ $87$ $C_{87}$ $C_1$ $C_1$ $C_{87}$ Cyclic
91.1 $C_{91}$ $7 \cdot 13$ $7 \cdot 13$ $91$ $C_{91}$ $C_1$ $C_1$ $C_{91}$ Cyclic
93.2 $C_{93}$ $3 \cdot 31$ $3 \cdot 31$ $93$ $C_{93}$ $C_1$ $C_1$ $C_{93}$ Cyclic
94.2 $C_{94}$ $2 \cdot 47$ $2 \cdot 47$ $94$ $C_{94}$ $C_1$ $C_1$ $C_{94}$ Cyclic
95.1 $C_{95}$ $5 \cdot 19$ $5 \cdot 19$ $95$ $C_{95}$ $C_1$ $C_1$ $C_{95}$ Cyclic
102.4 $C_{102}$ $2 \cdot 3 \cdot 17$ $2 \cdot 3 \cdot 17$ $102$ $C_{102}$ $C_1$ $C_1$ $C_{102}$ Cyclic
105.2 $C_{105}$ $3 \cdot 5 \cdot 7$ $3 \cdot 5 \cdot 7$ $105$ $C_{105}$ $C_1$ $C_1$ $C_{105}$ Cyclic
106.2 $C_{106}$ $2 \cdot 53$ $2 \cdot 53$ $106$ $C_{106}$ $C_1$ $C_1$ $C_{106}$ Cyclic
110.6 $C_{110}$ $2 \cdot 5 \cdot 11$ $2 \cdot 5 \cdot 11$ $110$ $C_{110}$ $C_1$ $C_1$ $C_{110}$ Cyclic
111.2 $C_{111}$ $3 \cdot 37$ $3 \cdot 37$ $111$ $C_{111}$ $C_1$ $C_1$ $C_{111}$ Cyclic
114.6 $C_{114}$ $2 \cdot 3 \cdot 19$ $2 \cdot 3 \cdot 19$ $114$ $C_{114}$ $C_1$ $C_1$ $C_{114}$ Cyclic
115.1 $C_{115}$ $5 \cdot 23$ $5 \cdot 23$ $115$ $C_{115}$ $C_1$ $C_1$ $C_{115}$ Cyclic
118.2 $C_{118}$ $2 \cdot 59$ $2 \cdot 59$ $118$ $C_{118}$ $C_1$ $C_1$ $C_{118}$ Cyclic
119.1 $C_{119}$ $7 \cdot 17$ $7 \cdot 17$ $119$ $C_{119}$ $C_1$ $C_1$ $C_{119}$ Cyclic
122.2 $C_{122}$ $2 \cdot 61$ $2 \cdot 61$ $122$ $C_{122}$ $C_1$ $C_1$ $C_{122}$ Cyclic
123.1 $C_{123}$ $3 \cdot 41$ $3 \cdot 41$ $123$ $C_{123}$ $C_1$ $C_1$ $C_{123}$ Cyclic
129.2 $C_{129}$ $3 \cdot 43$ $3 \cdot 43$ $129$ $C_{129}$ $C_1$ $C_1$ $C_{129}$ Cyclic
130.4 $C_{130}$ $2 \cdot 5 \cdot 13$ $2 \cdot 5 \cdot 13$ $130$ $C_{130}$ $C_1$ $C_1$ $C_{130}$ Cyclic
133.1 $C_{133}$ $7 \cdot 19$ $7 \cdot 19$ $133$ $C_{133}$ $C_1$ $C_1$ $C_{133}$ Cyclic
134.2 $C_{134}$ $2 \cdot 67$ $2 \cdot 67$ $134$ $C_{134}$ $C_1$ $C_1$ $C_{134}$ Cyclic
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